What is the Least Common Multiple of 27700 and 27712?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 27700 and 27712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27700 and 27712, than apply into the LCM equation.

GCF(27700,27712) = 4
LCM(27700,27712) = ( 27700 × 27712) / 4
LCM(27700,27712) = 767622400 / 4
LCM(27700,27712) = 191905600

Least Common Multiple (LCM) of 27700 and 27712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27700 and 27712. First we will calculate the prime factors of 27700 and 27712.

Prime Factorization of 27700

Prime Factorization of 27712

Now multiplying the highest exponent prime factors to calculate the LCM of 27700 and 27712.

LCM(27700,27712) = 2⁶ × 5² × 277¹ × 433¹
LCM(27700,27712) = 191905600